Properties

Label 45968.t
Number of curves $4$
Conductor $45968$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 45968.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45968.t1 45968k4 \([0, -1, 0, -305608, 45037680]\) \(159661140625/48275138\) \(954428909873733632\) \([2]\) \(663552\) \(2.1551\)  
45968.t2 45968k3 \([0, -1, 0, -278568, 56675696]\) \(120920208625/19652\) \(388532021116928\) \([2]\) \(331776\) \(1.8085\)  
45968.t3 45968k2 \([0, -1, 0, -116328, -15229072]\) \(8805624625/2312\) \(45709649543168\) \([2]\) \(221184\) \(1.6058\)  
45968.t4 45968k1 \([0, -1, 0, -8168, -173200]\) \(3048625/1088\) \(21510423314432\) \([2]\) \(110592\) \(1.2592\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 45968.t have rank \(0\).

Complex multiplication

The elliptic curves in class 45968.t do not have complex multiplication.

Modular form 45968.2.a.t

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 4 q^{7} + q^{9} + 6 q^{11} - q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.